Inventory Control. Chapter 15. OBJECTIVES . Inventory System Defined Inventory Costs Independent vs. Dependent Demand Single-Period Inventory Model Multi-Period Inventory Models: Basic Fixed-Order Quantity Models Multi-Period Inventory Models: Basic Fixed-Time Period Model
1. To maintain independence of operations
2. To meet variation in product demand
3. To allow flexibility in production scheduling
4. To provide a safeguard for variation in raw material delivery time
5. To take advantage of economic purchase-order size
Independent Demand (Demand for the final end-product or demand not related to other items)
(Derived demand items for component parts,
raw materials, etc)Independent vs. Dependent Demand
This model states that we should continue to increase the size of the inventory so long as the probability of selling the last unit added is equal to or greater than the ratio of: Cu/Co+Cu
Cu = $10 and Co= $5; P≤ $10 / ($10 + $5) = .667
Z.667 = .432 (use NORMSDIST(.667) or Appendix E)
therefore we need 2,400 + .432(350) = 2,551 shirts
1. You receive an order quantity Q.
2. Your start using them up over time.
3. When you reach down to a level of inventory of R, you place your next Q sized order.
R = Reorder point
Q = Economic order quantity
L = Lead timeBasic Fixed-Order Quantity Model and Reorder Point Behavior
TC=Total annual cost
C =Cost per unit
Q =Order quantity
S =Cost of placing an order or setup cost
R =Reorder point
L =Lead time
H=Annual holding and storage cost per unit of inventory
Using calculus, we take the first derivative of the total cost function with respect to Q, and set the derivative (slope) equal to zero, solving for the optimized (cost minimized) value of Qopt
We also need a reorder point to tell us when to place an order
Given the information below, what are the EOQ and reorder point?
Annual Demand = 1,000 units
Days per year considered in average
daily demand = 365
Cost to place an order = $10
Holding cost per unit per year = $2.50
Lead time = 7 days
Cost per unit = $15
In summary, you place an optimal order of 90 units. In the course of using the units to meet demand, when you only have 20 units left, place the next order of 90 units.
Determine the economic order quantity
and the reorder point given the following…
Annual Demand = 10,000 units
Days per year considered in average daily demand = 365
Cost to place an order = $10
Holding cost per unit per year = 10% of cost per unit
Lead time = 10 days
Cost per unit = $15
Place an order for 366 units. When in the course of using the inventory you are left with only 274 units, place the next order of 366 units.
q = Average demand + Safety stock – Inventory currently on hand
Given the information below, how many units should be ordered?
Average daily demand for a product is 20 units. The review period is 30 days, and lead time is 10 days. Management has set a policy of satisfying 96 percent of demand from items in stock. At the beginning of the review period there are 200 units in inventory. The daily demand standard deviation is 4 units.
The value for “z” is found by using the Excel NORMSINV function, or as we will do here, using Appendix D. By adding 0.5 to all the values in Appendix D and finding the value in the table that comes closest to the service probability, the “z” value can be read by adding the column heading label to the row label.
So, by adding 0.5 to the value from Appendix D of 0.4599, we have a probability of 0.9599, which is given by a z = 1.75
So, to satisfy 96 percent of the demand, you should place an order of 645 units at this review period
Based on the same assumptions as the EOQ model, the price-break model has a similar Qopt formula:
i = percentage of unit cost attributed to carrying inventory
C = cost per unit
Since “C” changes for each price-break, the formula above will have to be used with each price-break cost value
A company has a chance to reduce their inventory ordering costs by placing larger quantity orders using the price-break order quantity schedule below. What should their optimal order quantity be if this company purchases this single inventory item with an e-mail ordering cost of $4, a carrying cost rate of 2% of the inventory cost of the item, and an annual demand of 10,000 units?
0 to 2,499 $1.20
2,500 to 3,999 1.00
4,000 or more .98
First, plug data into formula for each price-break value of “C”
Annual Demand (D)= 10,000 units
Cost to place an order (S)= $4
Carrying cost % of total cost (i)= 2%
Cost per unit (C) = $1.20, $1.00, $0.98
Next, determine if the computed Qopt values are feasible or not
Interval from 0 to 2499, the Qopt value is feasible
Interval from 2500-3999, the Qopt value is not feasible
Interval from 4000 & more, the Qopt value is not feasible
Since the feasible solution occurred in the first price-break, it means that all the other true Qopt values occur at the beginnings of each price-break interval. Why?
Because the total annual cost function is a “u” shaped function
Total annual costs
So the candidates for the price-breaks are 1826, 2500, and 4000 units
0 1826 2500 4000 Order Quantity
Next, we plug the true Qopt values into the total cost annual cost function to determine the total cost under each price-break
Finally, we select the least costly Qopt, which is this problem occurs in the 4000 & more interval. In summary, our optimal order quantity is 4000 units
Actual Inventory Level, I
IMiscellaneous Systems:Optional Replenishment System
Maximum Inventory Level, M
Q = minimum acceptable order quantity
If q > Q, order q, otherwise do not order any.
60ABC Classification System
So, identify inventory items based on percentage of total dollar value, where “A” items are roughly top 15 %, “B” items as next 35 %, and the lower 65% are the “C” items